Subgroups — #11928140

Order 1248.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃₁₂	C₂	1	1	yes	maximal, characteristic
3	C₃⋊#6090	C₂	1	1	yes	maximal, characteristic, complemented
4	#88068	—	3	1	no	maximal, Hall
5	C₃×Q₈×C₁₃	—	2	1	no	—
6	D₁₅₆	—	2	1	no	—
7	C₃×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₁₃×Q₁₆	D₃	1	1	yes	characteristic, complemented
9	D₁₀₄	—	3	1	no	—
10	#6090	—	3	1	no	—
11	C₂×D₃₉	—	4	1	no	—
12	C₃×C₄×C₁₃	—	4	1	no	—
13	C₃×C₄×C₁₃	D₄	1	1	yes	characteristic
14	Q₈×C₁₃	—	2	1	no	—
15	D₅₂	—	6	1	no	—
16	C₈×C₁₃	C₂×D₃	1	1	yes	characteristic
17	#828	—	13	1	no	maximal, Hall
18	C₂×C₃×C₁₃	D₈	1	1	yes	characteristic
19	D₃₉	—	8	1	no	—
20	C₂×D₁₃	—	12	1	no	—
21	C₄×C₁₃	—	4	1	no	—
22	C₄×C₁₃	#67	1	1	yes	characteristic
23	C₃×Q₁₆	D₁₃	1	1	yes	characteristic, complemented
24	D₂₄	—	13	1	no	—
25	C₃⋊C₁₆	—	13	1	no	—
26	C₃×C₁₃	SD₃₂	1	1	yes	characteristic, complemented, Hall
27	SD₃₂	—	39	1	no	Sylow
28	C₂×C₁₃	#213	1	1	yes	characteristic
29	D₁₃	—	24	1	no	—
30	C₃×Q₈	—	2	1	no	—
31	D₁₂	—	26	1	no	—
32	C₃×C₈	C₂×D₁₃	1	1	yes	characteristic
33	Q₁₆	D₃₉	1	1	yes	characteristic, complemented
34	D₈	—	39	1	no	—
35	C₁₆	—	39	1	no	—
36	C₁₃	#828	1	1	yes	characteristic, complemented, Sylow
37	C₂×D₃	—	52	1	no	—
38	C₃×C₄	—	4	1	no	—
39	C₃×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
40	Q₈	—	2	1	no	—
41	D₄	—	78	1	no	—
42	C₈	C₂×D₃₉	1	1	yes	characteristic
43	C₂×C₃	#6104	1	1	yes	characteristic
44	D₃	—	104	1	no	—
45	C₂²	—	156	1	no	—
46	C₄	—	4	1	no	—
47	C₄	#64625	1	1	yes	characteristic
48	C₃	#88068	1	1	yes	characteristic, complemented, Sylow
49	C₂	—	312	1	no	—
50	C₂	#10597667	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#10597667
commutator, cosocle	C₃×C₈×C₁₃	C₂²
Frattini	C₈	C₂×D₃₉
Fitting	C₃×C₁₃×Q₁₆	C₂
socle	C₂×C₃×C₁₃	D₈
prime radical	D₃₁₂	C₂
hypercenter	Q₁₆	D₃₉
hypocenter	C₃×C₁₃	SD₃₂
LCS	G ▷ C₃×C₈×C₁₃ ▷ C₃×C₄×C₁₃ ▷ C₂×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₁₆

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃×C₁₃×Q₁₆	C₂	semidirect
3. C₃⋊#6090	C₂	semidirect
8. C₁₃×Q₁₆	D₃	semidirect
23. C₃×Q₁₆	D₁₃	semidirect
26. C₃×C₁₃	SD₃₂	semidirect
33. Q₁₆	D₃₉	semidirect
36. C₁₃	#828	semidirect
48. C₃	#88068	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₁₃×Q₁₆	2
D₃₁₂	2
C₃⋊#6090	2
#88068	3
#828	13